Search results for " Intensity function"

Hybrid kernel estimates of space-time earthquake occurrence rates using the Etas model

2010

The following steps are suggested for smoothing the occurrence patterns in a clustered space–time process, in particular the data from an earthquake catalogue. First, the original data is fitted by a temporal version of the ETAS model, and the occurrence times are transformed by using the cumulative form of the fitted ETAS model. Then the transformed data (transformed times and original locations) is smoothed by a space–time kernel with bandwidth obtained by optimizing a naive likelihood cross-validation. Finally, the estimated intensity for the original data is obtained by back-transforming the estimated intensity for the transformed data. This technique is used to estimate the intensity f…

Probabilistic Forecast for Northern New Zealand Seismic Process Based on a Forward Predictive Kernel Estimator

2011

In seismology predictive properties of the estimated intensity function are often pursued. For this purpose, we propose an estimation procedure in time, longitude, latitude and depth domains, based on the subsequent increments of likelihood obtained adding an observation one at a time. On the basis of this estimation approach a forecast of earthquakes of a given area of Northern New Zealand is provided, assuming that future earthquakes activity may be based on the smoothing of past earthquakes.

Comparison between nonparametric and parametric estimate of the conditional intensity function of a seismic space-time point process

2008

A seismic gap can be defined as a segment of an active geologic fault that has not produced seismic events for an unusually long time; gaps are often considered susceptible to future strong earthquakes occurrence and therefore their identification may be useful for predictive purposes. In this paper we try to identify gaps in an area of South Tyrrhenian Sea by comparing the observed seismicity, estimated by nonparametric method, and the theoretical one, described by a particular space-time point process (ETAS model).

Point process diagnostics based on weighted second-order statistics and their asymptotic properties

2008

A new approach for point process diagnostics is presented. The method is based on extending second-order statistics for point processes by weighting each point by the inverse of the conditional intensity function at the point’s location. The result is generalized versions of the spectral density, R/S statistic, correlation integral and K-function, which can be used to test the fit of a complex point process model with an arbitrary conditional intensity function, rather than a stationary Poisson model. Asymptotic properties of these generalized second-order statistics are derived, using an approach based on martingale theory.

An algorithm for earthquakes clustering based on maximum likelihood

2007

In this paper we propose a clustering technique set up to separate and find out the two main components of seismicity: the background seismicity and the triggered one. We suppose that a seismic catalogue is the realization of a non homogeneous space-time Poisson clustered process, with a different parametrization for the intensity function of the Poisson-type component and of the clustered (triggered) component. The method here proposed assigns each earthquake to the cluster of earthquakes, or to the set of independent events, according to the increment to the likelihood function, computed using the conditional intensity function estimated by maximum likelihood methods and iteratively chang…

Semi-parametric estimation of conditional intensity functions in inhomogeneous space-time point processes

2009

Dealing with data coming from a space-time inhomogeneous process, there is often the need of obtaining estimates of the conditional intensity function, without a complete defi nition of a parametric model and so nonparametric estimation is required: isotropic or anisotropic kernel estimates can be used. The properties of the intensities estimated are not always good, expecially in seismological field. We could try to choose the bandwidth in order to have good predictive properties of the estimated intensity function. Since a direct ML approach can not be followed, we use an estimation procedure based on the further increments of likelihood obtained adding a new observation. Similarly to cro…

Nonparametric intensity estimation in space-time point processes and application to seismological problems

2008

Space-Time Forecasting of Seismic Events in Chile

2017

The aim of this work is to study the seismicity in Chile using the ETAS (epidemic type aftershock sequences) space‐time approach. The proposed ETAS model is estimated using a semi‐parametric technique taking into account the parametric and nonparametric components corresponding to the triggered and background seismicity, respectively. The model is then used to predict the temporal and spatial intensity of events for some areas of Chile where recent large earthquakes (with magnitude greater than 8.0 M) occurred.

A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation

2018

We consider a time-non-homogeneous double-ended queue subject to catastrophes and repairs. The catastrophes occur according to a non-homogeneous Poisson process and lead the system into a state of failure. Instantaneously, the system is put under repair, such that repair time is governed by a time-varying intensity function. We analyze the transient and the asymptotic behavior of the queueing system. Moreover, we derive a heavy-traffic approximation that allows approximating the state of the systems by a time-non-homogeneous Wiener process subject to jumps to a spurious state (due to catastrophes) and random returns to the zero state (due to repairs). Special attention is devoted to the cas…